On the set of singularities of the Poincaré divisor of the Picard variety of the Fano surface of a nonsingular cubic

In the paper it is proved that the singular points of the Poincaré divisor of the Picard variety of the Fano surface of a nonsingular cubic are contained in the set of points of second and third orders of the abelian variety or in elliptic curves corresponding to the inflection points of the cubic.